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First, we need to recall 2 basic definitions of vector operations: The dot product is defined on vectors u =[u 1 , u 2 ,...u n ] and v =[v 1 , v 2 ,..., v n ] as u . v = u 1 v 1 +u 2 v 2 +...+u n v n The len...

Suppose you have a quadratic equation: x 2 + 5x + 6 You are told it has TWO REAL ROOTS and you are to find them. The factorised quadratic with two roots will look like this: (x+ a )(x+ b ) Where a and b are ...

To solve the equation: (5x+3)/(x) + x = 1, where (x) is the denominator, we have to convert the equation into an equation without any denominators. To do this, we multiply each variable by (x), so the equati...

The chain rule is used when you're trying to differentiate a complicated function, and it allows you to split up the function into easier ones. The trick is spotting where to split the function, and what par...

So you've encountered something like: g(x) = | 4 f( |x + 1| - 3 ) + 5 | What a mess! And you are only given the graph of f(x). How do we go about sketching g(x)? As in any problem in mathematics, let's break...